Pierre Biver

Uncertainties in Facies Proportion Estimation II: Application to Geostatistical Simulation of Facies and Assessment of Volumetric Uncertainties

Geostatistical simulations of lithotypes or facies are commonly used to create a geological model and to describe the heterogeneities of petroleum reservoirs. However, it is difficult to handle such models in the framework of multiple realizations to assess the uncertainty of hydrocarbon in place. Indeed, the hydrocarbon in place is correlated with the facies proportions, which are themselves uncertain. The uncertainty model of facies proportions is not easy to describe because of closure relationships. A previous attempt was made with a nonparametric approach using the resampling technique. It has been successful in a stationary case but it is difficult to extend it to nonstationary cases. In this paper, we have applied the vectorial beta parametric model or Dirichlet model. It has provided much more realistic uncertainties on volumetrics in very different geological and geostatistical contexts.

Constraining distance-based multipoint simulations to proportions and trends

In the last years, the use of training images to represent spatial variability has emerged as a viable concept. Among the possible algorithms dealing with training images, those using distances between patterns have been successful for applications to subsurface modeling and earth surface observation. However, one limitation of these algorithms is that they do not provide a precise control on the local proportion of each category in the output simulations. We present a distance perturbation strategy that addresses this issue. During the simulation, the distance to a candidate value is penalized if it does not result in proportions that tend to a target given by the user. The method is illustrated on applications to remote sensing and pore-scale modeling. These examples show that the approach offers increased user control on the simulation by allowing to easily impose trends or proportions that differ from the proportions in the training image. A method to control local proportions with training image based geostatistical simulations.Allows imposing non-stationary features in the presence of a stationary training image.Global as well as local proportions can be accurately controlled.

Change-of-Support Models on Irregular Grids for Geostatistical Simulation

In many domains, numerical models are initialized with inputs defined on irregular grids. In petroleum reservoir engineering, they consist of a great variety of grid cells of different size and shape to enable fine-scale modeling in the vicinity of the wells and coarse modeling in less important regions. Geostatistical simulation algorithms, which are used to populate the cells of unstructured grids, often have to address the problem of transition from the small-scale statistical data stemming from laboratory cores analysis and seismic processing to the multiple larger scale geological supports. The reasonable generalization of the above-mentioned problem is integrating the point-support data to simulations on irregular supports. Classical geostatistical simulation methods for generating realizations of a stationary Gaussian random function cannot be applied to unstructured grids directly, because of the uneven supports. This article provides a critical review of existing geostatistical simulation methodologies for unstructured grids, including fine-scale simulations with upscaling and direct sequential simulation algorithms, and presents two different generalizations of the discrete Gaussian model for this purpose, thereby discussing the theoretical assumptions and the accuracy when implementing these models.

Handling Soft Probabilities in Multiple Point Statistics Simulation

This paper is presenting a methodology to handle rigorously soft probabilities in Multiple Point Statistics (MPS) simulation for facies modeling. It is based on the second generation algorithm for MPS simulation using efficient Direct Sampling of the training image. The soft probabilities are considered as local target proportions corresponding to a support size defined by a radius of influence. The acceptation of a data event found in the training image is tempered by its consistency with the target probabilities. Test results are presented to illustrate the efficiency of the technique.

Sorting Reservoir Models According to Flow Criteria: A Methodology, Using Fast Marching Methods and Multi-Dimensional Scaling

In this paper, we will present a two-step methodology to efficiently select a subset of models representative of the variety of dynamic behaviors for a large set of models. We will use different proxies to quickly approximate the flow simulator responses. A suggested first proxy is based on volumes connected to the wells. Another suggested proxy is based on the Fast Marching algorithm. It computes a front propagation from the wells to the rest of the reservoir.The methodology also uses Multi-Dimensional Scaling and kernel clustering to select a small number of models for real flow simulator. Finally, we compare Q10, Q50 and Q90 for the subset and for the entire set of models in order to validate the proxy and the model selection.

Hydrocarbonate Reservoir Characterization Constrained to Seismic Attributes

Introduction The growing difficulties encountered in petroleum exploration and production, such as declining discoveries, increasing coastal distances and field depth, create a constant need for innovation. To improve the knowledge and dominate reservoirs located in remote areas, new tools and methodologies must be developed. With the steady increase in computing power and the birth of new algorithms, this demand can be satisfied and project risks can be reduced.

Fast and Interactive Editing Tools for Spatial Models

Multiple point statistics (MPS) algorithms allow generation of random fields reproducing the spatial features of a training image (TI). Although many MPS techniques offer options to prescribe characteristics deviating from those of the TI (e.g., facies proportions), providing a TI representing the target features as well as possible is important. In this paper, methods for editing stationary images by applying a transformation—painting or warping—to the regions, similar to a representative pattern selected by the user in the image itself, are proposed. Painting simply consists in replacing image values, whereas warping consists in deforming the image grid (compression or expansion of similar regions). These tools require few parameters and are interactive: the user defines locally how the image should be modified, then the changes are propagated automatically to the entire image. Examples show the ability of the proposed methods to keep spatial features consistent within the entire edited image.

Geostatistics on Unstructured Grids, Theoretical Background, and Applications

Traditionally, geostatistical simulations are performed on regular grids, in IJK coordinates system, simulating centroids of the cells. This approach (commonly used) has severe drawbacks: the support size effect is not taken into account and some artifacts due to cells distortion may appear. On the other hand, reservoir engineers and hydrogeologists are increasingly referring to new generation of grids to perform dynamic simulation (Voronoi grids, tetrahedral grids, etc.) which require addressing the volume support effect.

Geostatistical Simulations on Irregular Reservoir Models Using Methods of Nonlinear Geostatistics

SUMMARY Classical approaches to geostatistical simulations are not applicable directly on irregular reservoir models (such as Voronoi polygon and tetrahedron meshed models). One of the main difficulties is that the block marginal distributions are unique for every block due to volume support effect. We propose a methodology for geostatistical simulations which overcomes this difficulty in an analytical manner and provides a robust utilization of the small support petrophysical property distribution and the covariance model for irregular reservoir models. The proposed solution is based on the discrete Gaussian (DGM) model and operates directly on blocks of the target grid. This solution is also capable to improve the quality of the classical reservoir models, such as tartan meshes, by including the volume support effect into consideration and thus-providing geologically more realistic results. Applications to Voronoi polygon grid with local grid refinements and to a tartan-meshed offshore gas reservoir model are demonstrated.